diff --git a/NEWS.md b/NEWS.md
index 19ffbbf7..cb22566b 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -8,6 +8,8 @@
 
 * `parameters()` and the `grid_*()` functions give more information in the error message when non-parameter objects are passed in (#437, #438).
 
+* Improved several type-checking error messages to include the actual type of the input (#423).
+
 * `encode_unit()` now provides a helpful error when `x` is not a parameter object (#430).
 
 * `value_validate()`, `value_transform()`, `value_inverse()`, and `value_set()` now produce more informative error messages when values contain unknowns (#445).
diff --git a/R/encode_unit.R b/R/encode_unit.R
index 58986ade..0c50b917 100644
--- a/R/encode_unit.R
+++ b/R/encode_unit.R
@@ -19,10 +19,7 @@ encode_unit <- function(x, value, direction, ...) {
 
 #' @export
 encode_unit.default <- function(x, value, direction, ...) {
-  cli::cli_abort(
-    "{.arg x} should be a dials parameter object,
-    not {.obj_type_friendly x}."
-  )
+  stop_input_type(x, "a dials parameter object")
 }
 
 #' @rdname encode_unit
@@ -35,7 +32,7 @@ encode_unit.quant_param <- function(x, value, direction, original = TRUE, ...) {
   }
 
   if (!is.numeric(value) || is.matrix(value)) {
-    cli::cli_abort("{.arg value} should be a numeric vector.")
+    stop_input_type(value, "a numeric vector")
   }
 
   param_rng <- x$range$upper - x$range$lower
@@ -83,7 +80,7 @@ encode_unit.qual_param <- function(x, value, direction, ...) {
     # convert to [0, 1]
 
     if (!is.character(value) || is.matrix(value)) {
-      cli::cli_abort("{.arg value} should be a character vector.")
+      stop_input_type(value, "a character vector")
     }
 
     compl <- value[!is.na(value)]
@@ -107,7 +104,7 @@ encode_unit.qual_param <- function(x, value, direction, ...) {
     }
 
     if (!is.numeric(value) || is.matrix(value)) {
-      cli::cli_abort("{.arg value} should be a numeric vector.")
+      stop_input_type(value, "a numeric vector")
     }
 
     ind <- cut(
diff --git a/R/grids.R b/R/grids.R
index 477262ea..f9c0d875 100644
--- a/R/grids.R
+++ b/R/grids.R
@@ -407,11 +407,7 @@ make_random_grid <- function(
 # ------------------------------------------------------------------------------
 
 new_param_grid <- function(x = new_data_frame()) {
-  if (!is.data.frame(x)) {
-    cli::cli_abort(
-      "{.arg x} must be a data frame to construct a new grid from."
-    )
-  }
+  check_data_frame(x)
 
   x <- vctrs::vec_unique(x)
   size <- vctrs::vec_size(x)
diff --git a/R/misc.R b/R/misc.R
index 17c1cfdf..3c45dbc9 100644
--- a/R/misc.R
+++ b/R/misc.R
@@ -146,7 +146,7 @@ check_values_quant <- function(
   }
 
   if (!is.numeric(x)) {
-    cli::cli_abort("{.arg {arg}} must be numeric.", call = call)
+    stop_input_type(x, "a numeric vector", arg = arg, call = call)
   }
 
   if (anyNA(x)) {
diff --git a/tests/testthat/_snaps/constructors.md b/tests/testthat/_snaps/constructors.md
index 992839c8..6aa1cc43 100644
--- a/tests/testthat/_snaps/constructors.md
+++ b/tests/testthat/_snaps/constructors.md
@@ -316,7 +316,7 @@
       new_quant_param(type = "integer", values = "not_numeric", label = c(foo = "Foo"))
     Condition
       Error:
-      ! `values` must be numeric.
+      ! `values` must be a numeric vector, not the string "not_numeric".
 
 ---
 
diff --git a/tests/testthat/_snaps/encode_unit.md b/tests/testthat/_snaps/encode_unit.md
index 22bfa7ee..69e334f2 100644
--- a/tests/testthat/_snaps/encode_unit.md
+++ b/tests/testthat/_snaps/encode_unit.md
@@ -12,7 +12,7 @@
       encode_unit(prune_method(), 13, direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a character vector.
+      ! `value` must be a character vector, not the number 13.
 
 # to [0, 1] for quantitative values
 
@@ -20,7 +20,7 @@
       encode_unit(penalty(), "penalty", direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a numeric vector.
+      ! `value` must be a numeric vector, not the string "penalty".
 
 # encode_unit validates original argument
 
@@ -36,7 +36,7 @@
       encode_unit("foo")
     Condition
       Error in `encode_unit()`:
-      ! `x` should be a dials parameter object, not a string.
+      ! `x` must be a dials parameter object, not the string "foo".
 
 ---
 
@@ -44,7 +44,7 @@
       encode_unit(2, prune_method()$values, direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `x` should be a dials parameter object, not a string.
+      ! `x` must be a dials parameter object, not the number 2.
 
 ---
 
@@ -61,7 +61,7 @@
       encode_unit(x, prune_method()$values, direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a numeric vector.
+      ! `value` must be a numeric vector, not a character vector.
 
 ---
 
@@ -69,7 +69,7 @@
       encode_unit(z, 1, direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a character vector.
+      ! `value` must be a character vector, not the number 1.
 
 ---
 
@@ -77,7 +77,7 @@
       encode_unit(x, matrix(letters[1:4], ncol = 2), direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a numeric vector.
+      ! `value` must be a numeric vector, not a character matrix.
 
 ---
 
@@ -85,7 +85,7 @@
       encode_unit(x, matrix(1:4, ncol = 2), direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a numeric vector.
+      ! `value` must be a numeric vector, not an integer matrix.
 
 ---
 
@@ -93,7 +93,7 @@
       encode_unit(z, matrix(1:4, ncol = 2), direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a character vector.
+      ! `value` must be a character vector, not an integer matrix.
 
 ---
 
@@ -101,7 +101,7 @@
       encode_unit(z, matrix(letters[1:4], ncol = 2), direction = "forward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a character vector.
+      ! `value` must be a character vector, not a character matrix.
 
 ---
 
@@ -109,7 +109,7 @@
       encode_unit(x, prune_method()$values, direction = "backward")
     Condition
       Error in `encode_unit()`:
-      ! `value` should be a numeric vector.
+      ! `value` must be a numeric vector, not a character vector.
 
 ---
 
diff --git a/tests/testthat/_snaps/grids.md b/tests/testthat/_snaps/grids.md
index 570203b8..344efc88 100644
--- a/tests/testthat/_snaps/grids.md
+++ b/tests/testthat/_snaps/grids.md
@@ -397,5 +397,5 @@
       new_param_grid(as.matrix(x))
     Condition
       Error in `new_param_grid()`:
-      ! `x` must be a data frame to construct a new grid from.
+      ! `x` must be a data frame, not an integer matrix.
 
diff --git a/tests/testthat/_snaps/misc.md b/tests/testthat/_snaps/misc.md
index d2f03fbe..1e8c054d 100644
--- a/tests/testthat/_snaps/misc.md
+++ b/tests/testthat/_snaps/misc.md
@@ -20,7 +20,7 @@
       check_values_quant("should have been a numeric")
     Condition
       Error:
-      ! `"should have been a numeric"` must be numeric.
+      ! `"should have been a numeric"` must be a numeric vector, not the string "should have been a numeric".
 
 ---